Digital sampling oscilloscopes (DSOs) generally fall into one of two broad classifications, real time DSO's and equivalent time DSO's. Digital Sampling Oscilloscopes from both classifications sample the analog values of an input signal and then input those samples to an analog to digital converter (ADC), whereupon the resultant digitized values are stored in a memory called an acquisition record.
Real time digital oscilloscopes produce a trace each time they are triggered. They tend to have expensive high performance architectures that are capable of consecutively sampling at high speed a large number of locations along an input waveform. One of their valuable assets is the ability to be triggered for a single event (a single shot), or perhaps infrequently occurring event, thereby providing a detailed record of a non-repetitive, high speed event.
In contrast, equivalent time digital sampling oscilloscopes rely upon the repetitive nature of the input waveform. Different parts of the repetitive input waveform are digitized for each of a series of consecutive triggers. The acquisition records are then combined to produce an equivalent acquisition record.
In both cases there are often elaborate mechanisms that take the completed acquisition record and process the data therein for presentation in a display, which is commonly a raster scan mechanism driven from a frame buffer. A fair degree of complexity resides in selecting and massaging data in the acquisition record and forming it into a displayable image in the frame buffer. The user typically has capability of selecting, after the fact, the time scale (zooming in and out along the X axis) and voltage scale (zooming in and out along the Y axis) with which the trace is to be rendered on the monitor of the oscilloscope. Often this means extensive interpolation, since there is no particular correspondence between the time and voltage granularity with which the sampled, processed data is stored in the acquisition record and the pixel-to-pixel position spacing in the raster scan display mechanism that is to exhibit the trace. In order to display a realistic appearing trace, holes in the displayed trace caused by sampled data falling on either side of a pixel location should not be allowed to occur. In addition, it is common for the trigger event to be located following the start of the acquisition record (negative time) and for the location of the trigger event relative to the start of the displayed portion of the trace to be adjustable (panning).
As digital oscilloscopes are developed to operate at higher and higher frequencies, new classes of difficulties emerge. One such difficulty may be classed as “frequency response” which reveals itself as combination of different causes but which tend to have a similar result: the measured amplitude of a signal is incorrect, and it is the bandwidth consuming components of signals that account for the errors. For example, there is a simple frequency response, where, for example, there is a shunt capacitance that is not compensated in view of a series resistance, resulting in an RC filter. Or, perhaps an amplifier is bandwidth limited, and its frequency response rolls off sooner than desired. Another example is reflected power caused by discontinuities in the transmission lines used to couple the system or device under test to the oscilloscope. While this is a useful phenomenon that is the basis for TDR (Time Domain Reflectometry), and TDR results are often easy to interpret when there is limited bandwidth or only one or two reflections, reflected power also re-reflects off ALL the other discontinuities. The more bandwidth and the greater the voltage resolution the measurement system has, the worse the results appear. When these same results are manifested in a time domain trace of a voltage waveform under measurement, the result often appears to be an unpredictably uneven frequency response that gives the waveform properties that appear to be spurious artifacts. Another source of frequency dependent errors are various absorptive and dissipative losses in the transmission media.
To address these performance issues, high end digital sampling oscilloscopes of different designs or model numbers have been characterized to discover a particular digital signal processing (DSP) transform, which, for that particular model oscilloscope flattens its frequency response. A more expensive approach is to individually characterize each instrument produced, and then provide it with its own custom compensatory DSP transform. In either case, the DSP techniques used in the transforms are capable of correcting each of the error mechanisms mentioned above, singly and in combination. However, they impose requirements on the manner in which an acquisition record was produced. One such requirement is that all samples in the acquisition record should have equal spacing along a time axis due to the fact that viable DSP techniques typically require regularly spaced samples.
Obtaining samples that are equally spaced in time can be obtained fairly easily for a real time digital sampling oscilloscope, at least for a single acquisition record. So long as there is just one acquisition record contributing to a trace, the acquisition record is compensated by DSP and the result given to the rendering system for display according to the user's settings. Traces requiring higher bandwidths require more samples per second with associated greater memory for storage of the digitized samples and resultant economic penalty.
An alternative and for some situations more economically viable approach for repetitive waveforms is to use an equivalent time (ET) digital sampling oscilloscope. An equivalent time digital sampling oscilloscope takes, for a first trigger, a set of samples of a first portion of the input waveform, and then for a subsequent trigger another set of samples for a second (different) portion of the waveform (by a judicious application of a selected delay after the subsequent trigger), and so on, until we have a collection of acquisition records (one record per sample set) that, when taken in the proper sequence, describe the measured waveform of interest.
In its simplest form, equivalent time is simply combining data from multiple acquisitions. However, there are two traditional types of equivalent time oscilloscopes. The first traditional method is typically used on very high bandwidth sampling oscilloscopes in the many 10s of GHz of bandwidth. This method uses sequential sampling. It waits for a trigger, delays a programmable amount of time after the trigger, then takes a sample. Often, multiple samples are taken at a fixed spacing from the first, but the sample spacing is very wide relative to a real time scope. Most of the time these additional samples aren't even used as the time window wasn't wide enough. On the next trigger, the delay is programmed a little longer, and so on, so that a waveform usually builds from left to right, one sample per trigger. This method provides very little, if any, negative time. The second traditional method uses random sampling. This method samples at a programmable frequency, which is fixed during an acquisition, so that all samples are equally spaced. The time from the trigger to the sample clock is measured to determine how the samples will map to the display. The trigger also initiates the sequence that stops the sampling after a pre-determined amount of time. This time determines how much positive time is available. Depending upon the sample rate and the desired time window, one or more equally spaced samples may add to the equivalent time record. In order to cover larger time windows, the sample rate is slowed down. Data from each trigger covers the entire display, but the data is sparse. Multiple acquisitions eventually fill in the display. This method is referred to as random sampling because the positions of the samples are random (but within one sample period) with respect to the trigger, and this time must be measured.
Note that equivalent time techniques are not applicable to single shot traces due to the necessity of multiple triggers. Also note that not all samples will have originated on the same part of the time axis that will be used to display the trace.
Merging the various sets of samples and at the same time maintaining equal spacing of the samples is in a practical sense impossible. Within each of the several acquisition records the samples will be equally spaced in time, but the acquisition records as entities have, (despite the judicious known, after-trigger delays) essentially arbitrary amounts of time between when one ends and the next one starts. (Even if corrections are made for the time used to await a next trigger and the subsequent delay to position the upcoming acquisition record at the place in the incoming waveform that is where the next segment of samples is to occur, an arbitrary amount of time which is less than one sample period still remains.) Thus, one cannot simply merge all the samples into one big acquisition record for compensation by DSP techniques.
Additional effects, such as trigger jitter, also mitigate against attempts at such a merger of individual acquisition records. First, there is trigger jitter. Even if the input signal were quite stable and exhibited excellent repeatability (i.e., after a trigger the locations of successive events along the waveform of interest are always the same as they were for a previous trigger), the oscilloscope is not equipped with the ability to resume a sequence of samples with exactly the same delay after the next trigger as there was for the previous trigger. The timing of the samples is driven by a stable, yet free running, oscillator whose phase cannot be reset at will while it is running. This is a significant effect, since the time base of the oscilloscope and that of the system under test have no obligation to be related to each other. In addition, the waveform of interest may not have good periodicity, anyway. So the samples might not line up, no matter what we do, when some samples are taken from one instance of the signal and others from other instances.